91Ó°ÊÓ

To find the y-intercept of a linear equation, you need to set the value of x to 0. This is because the y-intercept is the point where the line crosses the y-axis, and on the y-axis, the x-coordinate is always 0. Let's use the given equation, \( y = \frac{1}{5}x + 2 \), as an example.

Step-by-step, it will look like this:
1. Substitute x = 0 into the equation:
\( y = \frac{1}{5}(0) + 2 \).
2. Simplify the equation:
\( y = 0 + 2 \).
3. So, \( y = 2 \).
Therefore, the y-intercept is (0, 2). This means the line crosses the y-axis at the point (0, 2).

Understanding y-intercepts is crucial, as it is one of the main descriptors of a linear equation along with the slope. Always remember: to find the y-intercept, set x to 0 and solve for y.

Finding the x-intercept involves setting the value of y to 0 in the equation. This is because the x-intercept is the point where the line crosses the x-axis, and on the x-axis, the y-coordinate is always 0. Let's go through the steps using the formula \( y = \frac{1}{5}x + 2 \).

Here's how to do it:
1. Substitute y = 0 into the equation:
\( 0 = \frac{1}{5}x + 2 \).
2. To isolate x, we first subtract 2 from both sides:
\( -2 = \frac{1}{5}x \).
3. Next, multiply both sides by 5 to solve for x:
\( x = -10 \).
Therefore, the x-intercept is (-10, 0). This tells us that the line crosses the x-axis at the point (-10, 0).

The x-intercept is useful for graphing the line and understanding its behavior. Always remember: to find the x-intercept, set y to 0 and solve for x.

Solving linear equations often involves manipulation to isolate the variable of interest. This can include using basic arithmetic operations such as addition, subtraction, multiplication, and division.

To understand this better, let's consider our example equation \( y = \frac{1}{5}x + 2 \). We already discussed how this equation can be used to find the intercepts by resolving it for y or x.

Here are the general steps to solve linear equations:

• Identify the variable you need to solve for.
• Use arithmetic operations to isolate the variable on one side of the equation.
• Make sure to do the same operation on both sides of the equation to maintain its equality.
• Continue simplifying until the variable is isolated.

Practicing with different linear equations will strengthen your understanding and confidence in solving them. Always take it step by step, and don't rush through the process. This methodical approach will help you with more complex equations in the future.